Parallel Graph Drawing Algorithm for Bipartite Planar Graphs
Naman Jain

TL;DR
This paper presents a parallel algorithm that efficiently assigns segments to vertices of bipartite planar graphs, enabling intersection-based representation while avoiding crossings, within logarithmic time on a CRCW PRAM.
Contribution
It introduces a novel parallel algorithm for segment assignment in bipartite planar graphs with optimal logarithmic time complexity.
Findings
Achieves $O( ext{log}(n))$ parallel time complexity.
Uses polynomial number of processors.
Ensures segments intersect iff vertices are adjacent.
Abstract
We give a parallel -time algorithm on a CRCW PRAM to assign vertical and horizontal segments to the vertices of any planar bipartite graph in the following manner: i) Two segments cannot share an interior point ii) Two segments intersect if and only if the corresponding vertices are adjacent, which uses a polynomial number of processors. In other words, represent vertices of a planar bipartite graph as parallel segments, and edges as intersection points between these segments. Note that two segments are not allowed to cross. Our method is based on a parallel algorithm for st-numbering which uses an ear decomposition search.
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Taxonomy
TopicsGraph Theory and Algorithms · Computational Geometry and Mesh Generation · Model-Driven Software Engineering Techniques
